随机游动法在环状河网计算中的应用研究

Study on application of random walk method in looping river network computation

环状河网求解不同于树状河网,在采用三级解法进行环状河网非恒定流计算时常面临求解大型矩阵的难题.针对这一问题,从水流质点游动角度出发,研究将随机游动方法应用于环状河网水位计算,实现随机游动方法与三级解法相结合.在三级解法得到节点水位方程组基础上,给出节点水位的随机显式求解新方法,然后采用追赶法完成整个河网水位流量计算.与常规三级解法相比,该方法求解原理简单,避免了大型矩阵的直接求解.将新方法建立模型运用于西江下游河网计算,结果表明,该方法较常规方法在简化运算的同时提高了计算效率,并且与常规三级解法具有同样的精度.模型计算结果也量化了各节点水位之间的相对联系情况.

Compared with branch river network computation, it＇s necessary to overcome the difficulty in solving large matrix when the three steps method is applied in the unsteady flow computation in looping river network. Given this difficulty and according to the water random walk theory, a study on the application of random walk method in looping river network computation was completed, and then a new method to calculate the node water stage was proposed by combining random walk method with the three steps method. With equations of node water stage derived from the three steps method, the new method got the stage with an explicit random solution. After that, the chasing method was chosen to finish the river network computation. Compared with the conventional three steps method, the new method could simplify computation procedures while the large matrix solution was unnecessary. Applied in the Xijiang River Network, the new method improved the calculation efficiency with the same accuracy as the conventional one. In addition, the result could present the quantified relationship between each node stage.